Engineering Tunable, Low Latency Spatial Computation with Dual Input Quorum Sensing Promoters

Quorum sensing signals have evolved for population-level signaling in bacterial communities and are versatile tools for engineering cell–cell signaling in synthetic biology projects. Here, we characterize the spatial diffusion of a palette of quorum sensing signals and find that their diffusion in agar can be predicted from their molecular weight with a simple power law. We also engineer novel dual- and multi-input promoters that respond to quorum-sensing diffusive signals for use in engineered genetic systems. We engineer a promoter scaffold that can be adapted for activation and repression by multiple diffusers simultaneously. Lastly, we combine the knowledge on diffusion dynamics with the novel genetic components to build a new generation of spatial, stripe-forming systems with a simplified design, improved robustness, tuneability, and response time.


Diffusion model fitting and data processing
The raw microscopy images of Figure 1B were processed with a moving average filter of 120 x 120 pixels, to remove shading artefacts from tiling and to reduce the noise.The size of the images was 2780 x 4160 pixels, covering an area of 48 x 72 mm. Figure S1 shows the raw data, together with the smoothened data.

Dose-response assays
Cells were suspended in 2xYT agar (1.4% w/V) and induced with spatially homogenous concentrations of diffusers.Cells harbouring the mCherry reporter constructs together with the Plux, Prpa, Plas and Pcin promoters were treated with OC6, pC, OC12 and OHC14, respectively.The fluorescence was measured with a microscope 16 hours after induction.The average image fluorescence was plotted against inducer concentration, for three biological replicates (Figure S2).This data was used to map inducer concentration to fluorescence in the diffusion models.S1.Please note that the fluorescence levels for Plas/OC12 are not comparable with the other three datasets because a different exposure setting was used, see Methods.

Loss of lawn responsivity
The reporter cells were plated as a lawn in an agar (1.4% w/V) suspension, incubated at 37 °C and induced with a delay between 0 and 10 hours.Fluorescence was measured at the 24 hour timepoint.The fluorescence response was allowed to develop fully for all the conditions.A gradual decline in the fluorescence response was observed with an increasing delay (Figure S3).The decline in fluorescence was fitted with linear functions (OC6 R 2 = 0.68, F-stat.vs. constant model p < 0.1; OHC14 R 2 = 0.92, F-stat.p << 0.01).This delay effect was more pronounced for the Pcin response to OHC14, where the system stopped responding after 11.5 hours.The Plux/OC6 system stopped responding after 19.2 hours.Overall, the results show that as they age, cells become less sensitive to the inducer.Similar findings are reported in other studies 1 .2 Supplementary 2: Distance Assay

Measurement of the cellular response delay t cell
The distance assay relies on measuring the delay between inducer droplet application and fluorescence expression.This delay includes the time needed for the diffuser to travel and reach the cells (diffusive delay, t diff ), and the time needed for the cell to respond once the diffusor has reached (cellular delay, t cell ).The relationship between distance and diffusive delay was used to calculate the diffusion rate of the molecules, whereas the cellular delay was treated as a constant as is inferred below.
The cellular delay was quantified by growing a small droplet of cells on top of agar containing a known concentration of spatially homogenous inducer.In this experiment t diff is zero, allowing us to measure t cell in isolation.This experiment was performed with the Prpa/pC system.It was assumed that similar laws also hold for the OC6/Plux, OC12/Plas and OHC14/Pcin systems.
Fluorescence measurements were taken every 5 minutes with a microscope, and average image fluorescence was plotted against time (Figure S4A).The final fluorescence was plotted against concentration and fitted with a Hill function (Fig SX ).An arbitrary threshold was set to be just above the background fluorescence for each induction condition, and the time point at which the curves crossed this threshold was calculated and plotted against inducer concentration (Figure S4B).The data shows that t cell does not change significantly across the effective diffusor concentration range (10 -3 µM -10 3 µM).The fitted linear model is not significantly different from a constant model (F-stat.= 3.09; p = 0.177): t cell can thus be treated as a constant.

Advancement of the threshold concentration
At the centre of the model fitting strategy for the distance assay are simulations of the diffusion PDE (Eq.1).A typical solution of the diffusion equation is shown in Figure S5A.The coloured curves show the concentration of the diffuser in space for the successive timepoints of the simulation.A cross-section of a 2D simulation is plotted in one spatial dimension.The black horizontal line denotes the chosen threshold concentration c t .The advancement of the location of the threshold concentration front is plotted in Figure S5B.
The quadratic function of Eq. 4, describing the displacement of the diffusing molecule in time, fits the data well.
The advancement of the diffusing front is largely dependent on the diffusion rate D X and on the ratio between the initial and threshold concentrations c 0 /c t .Scaling both c 0 and c t by the same factor does not affect the shape of the quadratic relationship of Figure S5B.What matters is how the initial stimulus compares to the front concentration in relative terms.The simulation of the diffusion PDE was repeated over a grid of D X and c 0 /c t parameters.D X was initialised in the interval [0.1, 2] mm 2 /h, whereas c 0 /c t was initialised in [10 3 , 10 9 ] µM.The simulations were performed over a 50 x 50 grid of logarithmically spaced points.The simulations were performed over a discretised grid of 60 x 60 points, where the size of the spatial domain was 60 mm x 60 mm.The initial condition c 0 was fixed to 10 3 µM, with a radius of 1 mm.The threshold concentration c t was changed according to the value of the c 0 /c t parameter.The advancement of the c t front is plotted in time in Figure S6 for five values of D X and c 0 /c t .The front advances more rapidly both when diffusion rate D X is increased, and when the front concentration c t is decreased.Hence, both the diffusion and kinetics influence the spatial response to the inducer, fluorescence in our case.Quadratic functions of Eq. 4 fit all the simulations well.

Effect of agar concentration on diffusion rate
Agar concentration is inversely proportional to diffusion rate.Diffusion of urea slows by 36% when agar concentration is changed from 0.8 to 5.15% 2 .Similarly, diffusion rate of glycerin drops by 33% when increasing agar concentration from 2 to 6% 2 .We tested diffusion of OC6 in 0.4%, 1.4% and 2.4% agar using the distance-based assay (Figure S7).The diffusion of OC6 decreased by 40% when increasing agar concentration from 0.4% to 2.4%.The best fit models are shown with lines: these were obtained by simulating the diffusion PDE (Eq. 1) and plotting the advancement of the threshold concentration that leads to the minimal sensing event in space and time.The initial concentration of OC6 was 10 4 μM.The diffusion rates of OC6 in 2.4%, 1.4%, and 0.4% agar are 2.0, 2.4, and 3.4 mm 2 /h, respectively.While these values are largely consistent with those reported in the main paper, the small differences are likely due to small changes in the experimental protocols.This data had the cellular delay t cell subtracted for each agar concentration individually, the plot only shows diffusive delay t diff .

Repressible promoter variants
Promoters that are repressed by a single quorum sensing signal were designed first.The operators (Error!Reference source not found.)were placed immediately downstream a constitutive J23106 promoter.Some designs immediately showed strong repression (e.g.J23106-luxO), others showed intermediate repression (e.g.J23106-rpaO), and one showed no repression (e.g.J23106-cinO), see Fig. 3B.
To increase the repression levels multiple copies of the operators were placed in tandem downstream J23106.One, two and three copies were used for lasO.One, four and seven copies were tested for rhlO.The results were not as expected, where two operator copies showed a weaker repression compared to a single copy (Figure S8).Surprisingly, three or more copies reversed the effect and showed an induction rather than repression.This strategy of increasing repression strength was therefore abandoned.
Repression for single and double lasO variants was observed for both OC12 and OC16, consistent with observations that Prhl can sense multiple long chain AHLs 3 .

Figure S8: constitutive promoters J23106 combined with one or more quorums sensing operators.
A) One or more operators lasO and rhlO were placed downstream J23106 with short spacer sequences in between, followed by an RBS (darker grey) and the mCherry reporter gene.B) mCherry fluorescence after addition of OC16, OC12 for lasO variants, and C4 for rhlO variants at 100 µM.
To debug the non-functional J23106-cinO variant, we placed short segments of the Pcin promoter downstream J23106 to test their ability to repress.Using this approach, we obtained two functional variants, v1 and v2 (Figure S9).The v1 variant is weaker, but exhibits slightly stronger repression levels.On the other hand, the v2 variant preserves the constitutive activity of the J23106 promoter better, but displays slightly lower, even though comparable, fold-repression.

Dual-input promoter variants
The first series of dual-input promoter variants (HC1 series) was based on the designs put forward by Zucca et al. (2015) and Du et al. (2020), where the activating operator site is placed immediately upstream the promoter, whereas the repressing operator is placed immediately downstream or in the core promoter region (Figure S10) 4,5 .The HC1-5 promoter is the best in the series and shows strong activation by pC and tight repression by OC6; no activation is seen in the presence of OC6 alone, indicating no cross-talk between the operators.The HC1-6 promoter lost all activity probably owing to the strong luxO site being placed in the core promoter region.HC1-7 is another promising design, activated by OC6 and repressed by pC; the repression could be further optimised by tuning the rpaO site.HC1-8 shows very low activity when activated by OC6, and cannot be repressed by pC.HC1-9 and HC1-10 show good activation by OC6, but cannot be repressed by OHC14, probably owing to a dysfunctional cinO (Figure S9, iGEM site 6 , no activity seen in any of the designs), and could be optimised by using the cinO-v1 site.Overall, this shows that operators perform better in the distal, downstream site (rather than in the core region).Furthermore, the data shows that this architecture yields functional dual-input promoters; these could be further optimised by tuning the operator sites to increase their strength.The second series of dual-input promoters (HC2 series) involved placing operators into the Pcin promoter (iGEM R0078).Operators rpaO and luxO were placed in the core region and immediately downstream (Figure S11).The HC2-1 and HC2-2 promoters can be activated by OHC14 but show weak repression by rpaO; this is consistent with the weak repression levels that rpaO achieves when placed downstream J23106 (Fig. 3B).The HC2-3 promoter is the best in this series and shows good induction by OHC14 and repression by OC6.The HC2-4 promoter lost all activity, owing to the strong luxO site being placed inside the promoter.These promoters show promising results, but the strength of repression can be further optimised by tuning the operator sequences.

Supplementary 4: Ring Pattern Formation
The model for ring formation consisted of two steps.The first step involved solving the diffusion PDE for both the activator and inhibitor species and their diffusion rates D X .The result of one of these simulations is shown in Figure S12, where the inducers are spotted in the centre of the spatial domain and diffuse towards the periphery.The parameters in this example are D act = 0.6 and D inh = 0.9, consistent with the lawn diffusion rates of pC and OC6, respectively (Table 1).
The simulation results show that the ring forms and expands over time, due to the gradual diffusion of the molecules outwards (Figure S12E).This is however not observed in the experiments, where a ring of fixed diameter forms on the lawn of cells.This behaviour is analogous to the temporal evolution of mCherry fluorescence of Fig. 1C, where the bellshaped fluorescence distribution does not broaden with time, even though the molecules continue to diffuse outwards.The cellular lawn gives a snapshot of diffuser concentrations at a particular timepoint, which occurs sometime between t 0 and the time when the response reaches full induction, at about 10 hours (Figure S13B).The 10 hour timepoint was chosen when modelling the ring systems (Fig. 4C).This is also likely related to the dynamics of the loss of lawn responsivity, which also occurs at the 10 hour timepoint for the OHC14 system (Figure S3). ) Cellular response to the activator, obtained after feeding the activator concentrations through a Hill function fitted to the dose-response data of the HC1-5 promoter.D) Cellular response to the inhibitor over a fully activated lawn of cells, obtained after feeding the inhibitor concentrations through a Hill function of promoter HC1-5.The activator concentration was set to a value that produces full activation in the absence of the inhibitor.E) Cellular response to both the activator and inhibitor over a lawn of cells with the HC1-5 promoter.The timepoint of 10 h is highlighted in red because it was selected for the model simulations in Fig. 4. The size of the images is 43 mm x 43 mm, same as for Fig. 4C.
The second step of the modelling process for the ring patterns involved fitting a dual-input Hill function (Eq.S1) to the dose-response data of the underlying promoter, HC1-5 in our case.This model captures the data well (Figure S13).The best fit parameters are listed in Table S3.

Supplementary 5: DNA Sequences
In a nutshell, all the experiments were conducted by transforming cells with a pET reporter plasmid containing an mCherry reporter gene expressed under a promoter of interest, together with the pCC1R plasmid containing constitutively expressed receptor genes rpaR and cinR, which bind to the inducers and regulate the promoter activity.An additional p15A plasmid harbouring the luxR, lasR and rhlR genes was used when needed.
The pET and p15A are low-to-medium copy plasmids, whereas pCC1 (CopyControl plasmid) is close to single copy.

Full plasmid sequences
Legend: Promoter Operator RBS Terminator Gene

pET-Px
Universal backbone for inducer sensing (Section 1 and 2) and promoter testing (Section 3) constructs, mCherry is used as reporter.The Px sequences are listed in Tables S3-S5.

Figure S1 :
Figure S1: microscopy data smoothing with a moving average filter.A) Raw, unsmoothened data.B) Smoothened data.The display range for the images was adjusted to be between the minimum and maximum pixel intensity values for display purposes only.

Figure S2 :
Figure S2: dose-response assays in a lawn of cells suspended in agar.Average fluorescence levels in the microscope images are plotted against inducer concentration.Activating Hill functions (Eq.2) are fitted to the data, the parameters are listed in TableS1.Please note that the fluorescence levels for Plas/OC12 are not comparable with the other three datasets because a different exposure setting was used, see Methods.

Figure S3 :
Figure S3: gradual decline of fluorescence response with a delay in induction.The response of the Plux/OC6 (blue) and Pcin/OHC14 (green) system declines with increasing delay between plating and induction.The filled dots are the average fluorescence intensities of microscope images collected at the 24 hour timepoint.The dashed lines are the background fluorescence intensities for the uninduced conditions at 24 hours.The crosses are the intersections between the fitted lines and the background intensity, marking the time when the cells stop responding (19.2 h for OC6, 11.5 h for OHC14).

Figure S4 :
Figure S4: cellular response delay t cell .A) mCherry fluorescence evolution in time for different concentrations of inducer pC.The time at which the curves cross the black dashed line is the cellular

Figure S5 :
Figure S5: advancement of the threshold concentration in the diffusion PDE.A) A solution to the diffusion PDE from an initial condition c 0 of 10 3 µM with radius of 1 mm, D X = 1 mm 2 /h, over a period of 20 hours.The black horizontal line denotes the threshold concentration c t of 10 -2 µM.The points at the intersections between the coloured lines and the black line are the locations of the diffusing front at the c t concentration at the respective timepoints.B) Plots the advancement of the c t front in time.A quadratic relationship (Eq.4) fits the data well (red curve).

Figure S6 :
Figure S6: advancement of the threshold concentration front.The black points are derived from diffusion PDE simulations, by tracking the advancement of the c t concentration front in time and space.Both diffusion rate D X and threshold concentration c t affect the dynamics of front advancement.

Figure S7 :
Figure S7: effect of agar concentration on diffusion rate.Experimental results are shown with dots.The best fit models are shown with lines: these were obtained by simulating the diffusion PDE (Eq. 1) and plotting the advancement of the threshold concentration that leads to the minimal sensing event in space and time.The initial concentration of OC6 was 10 4 μM.The diffusion rates of OC6 in 2.4%, 1.4%, and 0.4% agar are 2.0, 2.4, and 3.4 mm 2 /h, respectively.While these values are largely consistent with those reported in the main paper, the small differences are likely due to small changes in the experimental protocols.This data had the cellular delay t cell subtracted for each agar concentration individually, the plot only shows diffusive delay t diff .

Figure S9 :
Figure S9: placing short segments of the Pcin promoter downstream J23106.A) The tested Pcin fragments (v1 -v9) are aligned to the Pcin promoter.The operator site identified by iGEM teams and Meyer et al. (2019) is labelled with 'iGEM'.The best site as determined by testing v1 -v9 is labelled with 'best'.The luxO was aligned with the Pcin sequence in the site labelled with 'align'.B) The v1 -v9 fragments were cloned downstream of J23106, the short RBS is shown in dark grey followed by the mCherry reporter gene.C) mCherry fluorescence levels.The v1, v2 and v3 promoters were successfully repressed by adding OHC14 at 10 µM (+) and 100 µM (++).

Figure S10 :
Figure S10: HC1 series of dual-input promoters.A) DNA architecture of the tested designs.B) mCherry fluorescence levels.The HC1-5 and HC1-7 promoters show good performance with induction and repression by their respective regulators.Concentration of inducers: 10 µM.

Figure S11 :
Figure S11: HC2 series of dual-input promoters.A) DNA architecture of the tested designs.B) mCherry fluorescence levels.The HC2-2 and HC2-3 promoters show good performance with induction and repression by their respective regulators, but can be improved by strengthening the repression arm.Concentration of inducers: 10 µM.

Figure S12 :
Figure S12: simulation of ring formation in time.A) Activator concentration in space, as obtained from the diffusion PDE simulation.B) Inhibitor concentration in space.C) Cellular response to the activator, obtained after feeding the activator concentrations through a Hill function fitted to the dose-response data of the HC1-5 promoter.D) Cellular response to the inhibitor over a fully activated lawn of cells, obtained after feeding the inhibitor concentrations through a Hill function of promoter HC1-5.The activator concentration was set to a value that produces full activation in the absence of

Figure S13 :
Figure S13: HC1-5 dose-response data and dual-input Hill function model fit.A) Timeseries absorbance measurements at 600 nm.Normal cell culture growth is detected for all inducer combinations.The system shows no toxicity or burden at any of the mCherry expression levels.B) Timeseries mCherry measurements, where a range of induction levels is observed for the different inducer combinations.The fluorescence response is fully developed approximately 11 hours after induction.The shape of the curves and the triphasic growth of fluorescence is likely due to the slow and multi-step maturation of the fluorophore 7 .C) Final mCherry levels plotted against pC and OC6 concentration, where 00 are the no-inducer controls.D) Dual-input Hill model reproduces the experimental data in C).

Table S1 :
Hill parameters obtained by fitting to dose-response data.

Table S3 :
fitted dual-input Hill function parameters.

Table S4 :
quorum sensing inducers used in this study, dissolved in DMSO at 10 to 50 mM.

Table S5 :
genetic part sequences derived from other studies.

Table S6 :
genetic sequences of the repressible promoters assembled and tested here.

Table S7 :
genetic sequences of the hybrid promoters assembled and tested here.
Plasmid for the expression of OC6, C4, and OC12 receptors, LuxR, RhlR and LasR (xR).Their sequences are provided below.Receptor array including the pC and OHC14 receptors RpaR and CinR.The AiiA lactonase gene is also present under an inducible PphlF promoter; this is not used in this study.